Detective Grant Miller, of Queenstown, said the Marlin lever-action 44 magnum calibre gun "went missing" from a delivery area in the Remarkables Park shopping complex on or about October 27.
Det Miller said the rifle, which is almost 1m long and weighs 2.9kg, was part of a delivery, but there was now "confusion" about its location.
Police were treating the rifle, worth about $1500, as stolen.
The rifle could hold 10 shots and had a distinctive octagonal 20-inch barrel.
The calibre of 44 magnum was also distinctive, Det Miller said.
"If it was old it would be used as a collector's item.
"Pig hunters would use it - it's got a short range and a reasonably big calibre. It's not a high-powered rifle."
Det Miller said there was no ammunition with the rifle.
Anyone with information was asked to contact the police confidentially.
• Queenstown police want to "reunite" a tent with its rightful owner.
Sergeant Brian Cameron, of Queenstown, said police found a tent "blowing down Frankton Rd near Suburb St" early on Wednesday morning.
"If the owner or the person who woke up in the morning without a tent above them wanted to contact police, we would be happy to reunite them."
• An incident involving "suspicious activity" in Queenstown on Wednesday morning was "clearly a matter of concern", Sgt Cameron said.
The occupants of a room at Flaming Kiwi Backpackers were woken between 4am and 5.30am "by someone shining a light through the window".
"[The occupant] woke up and the person has taken off."
It was a "matter of some concern" that someone was behaving in such a way, St Cameron said.
